Logic

What is logic?#

Logic is the analysis and appraisal of arguments.

I first encountered this via a philosophy lecturer I had in junior college, Lionel Barnard (he was actually supposed to teach Economics but preferred to turn our class into a little PPE program for our intellectual gratification).

In particular, I have always favored the format of syllogism, which takes a form like this:

• 1: All men are mortal.
• 2: All Greeks are men.
• Therefore: all Greeks are mortal.

“Therefore” denotes a logical and inevitable-to-the-point-of-truism consequence of the first two propositions. This underlies a lot of how proofs are done in math and the other basic sciences. Take N facts, put them together, derive a new, more useful fact that is as real as those other facts because it is built on top of them.

Supplant your syllogisms with axioms#

However, you can’t get very far if you only rely on facts because there are many more unknowns and indeterminate, or stochastic, processes than there are facts. So, you can supplant your syllogisms with axioms.

You don’t HAVE to prove them true, but you can show by deduction that given an acknowledged set of assumptions, you can arrive at a logically sound conclusion. This is FANTASTIC because it lets you enumerate your beliefs. It also allows you to change your mind instantly if your assumptions are proven wrong (especially handy because you can’t prove a negative).

Who would argue against logic?#

It turns out that logical deduction has limits and takes a lot more effort to corral facts (sometimes what you believe to be true isn’t, as in the replicability crisis) and validate the integrity of the logical chain of arguments. By far the most prevalent method we operate on is induction; we cover this in the Epistemology section.